Chemodynamical evolution of the Milky Way disk II ...

Astronomy & Astrophysics manuscript no. ms2 October 14, 2014(DOI: will be inserted by hand later)

Chemodynamical evolution of the Milky Way disk II: Variationswith Galactic radius and height above the disk plane

I. Minchev1, C. Chiappini1, M. Martig2,3

1 Leibniz-Institut fur Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482, Potsdam, Germany e-mail:[email protected]

2 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122,Australia

3 Max-Planck-Institut fur Astronomie, Konigstuhl 17, D-69117 Heidelberg, Germany

the date of receipt and acceptance should be inserted later

Abstract. In the first paper of this series (paper I) we presented a new approach for studying the chemodynamical evolution indisk galaxies, focusing on the MilkyWay. While in paper I we studied extensively the Solar vicinity, here we extend these resultsto different distances from the Galactic center, looking for variations of observables that can be related to on-going and futurespectroscopic surveys. By separating the effects of kinematic heating and radial migration, we show that migration is much moreimportant, even for the oldest and hottest stellar population. The distributions of stellar birth guiding radii and final guiding radii(signifying contamination from migration and heating, respectively) widen with increasing distance from the Galactic center.As a result, the slope in the age-metallicity relation flattens significantly at Galactic radii larger than solar. We predict thatthe metallicity distributions of (unbiased) samples at different distances from the galactic center peak at approximately thesame value, [Fe/H] ≈ −0.15 dex, and have similar metal-poor tails extending to [Fe/H] ≈ −1.3 dex. In contrast, the metal-richtail decreases with increasing radius, thus giving rise to the expected decline of mean metallicity with radius. Similarly, the[Mg/Fe] distribution always peaks at ≈ 0.15 dex, but its low-end tail is lost as radius increases, while the high-end tails off at[Mg/Fe] ≈ 0.45 dex. The radial metallicity and [Mg/Fe] gradients in our model show significant variations with height abovethe plane due to changes in the mixture of stellar ages. An inversion in the radial metallicity gradient is found from negativeto weakly positive (at r < 10 kpc), and from positive to negative for the [Mg/Fe] gradient, with increasing distance from thedisk plane. We relate this to the combined effect of (i) the predominance of young stars close to the disk plane and old starsaway from it, (ii) the more concentrated older stellar component, and (iii) the flaring of mono-age disk populations. We alsoinvestigate the effect of recycled gas flows on the mean [Fe/H] and find that in the region 4 < r < 12 kpc the introduced errorsare less than 0.05-0.1 dex, related to the fact that inward and outward flows mostly cancel in that radial range. We show thatradial migration cannot compete with the inside-out formation of the disk, exposed by the more centrally concentrated olderdisk populations, and consistent with recent observations.

1. Introduction

Galactic archeology aims at understanding the formation andevolution of the Milky Way (MW), where the chemical andkinematical information contained in its stellar component isused as fossil records (Freeman and Bland-Hawthorn, 2002;Matteucci, 2012). Unprecedented amounts of data from a num-ber of ongoing and planned astrometric and spectroscopicGalactic surveys (RAVE - Steinmetz 2012; SEGUE - Yannyand Rockosi 2009; HERMES - Freeman et al. 2010; APOGEE- Allende Prieto et al. 2008) will be available soon, especiallyfrom Gaia (Perryman et al., 2001) and 4MOST (de Jong et al.,2012), who together will provide high accuracy 6D kinematicsand chemistry for more than 107 disk stars.

It has been recently recognized that chemical evolutiongalactic disk modeling must be combined with dynamics. Themain reason for this is that numerical simulation have shown

that stars do not remain near their birth places, but migratethroughout the disk during their lifetimes. This redistributionof angular momentum has been shown to be caused by the ef-fect of non-axisymmetric disk features, such as spiral struc-ture (Sellwood and Binney, 2002; Roskar et al., 2008) and thecentral bar (Minchev and Famaey, 2010; Minchev et al., 2011;Brunetti et al., 2011; Di Matteo et al., 2013). This has resultedin efforts to understand how traditional, static, chemical evolu-tion disk modeling couples with dynamics, as discussed in de-tail in the introduction in the first paper of this series, Minchevet al. (2013) (hereafter paper I). We also refer the reader tothe comprehensive recent reviews by Rix and Bovy (2013) andBinney (2013).

2 I. Minchev et al.: Chemodynamical evolution of the Milky Way disk II

1.1. The chemodynamical model of paper I

The chemodynamicalmodel we use in this work was presentedin paper I, where we mostly concentrated on an annulus of2 kpc, centered on the “solar radius”. The main features thatmake this model unique is the fusion between a state-of-the-art simulation in the cosmological context (Martig et al., 2009,2012) and a detailed thin-disk chemical evolution model.

The exact star formation history and chemical enrichmentfrom our chemical model is implemented into the simulationwith more than 30 elements assigned to each particle. Thisnovel approach has made it possible to avoid problems withchemical enrichment and star formation rates currently foundin fully self-consistent simulations, as described in paper I.

The simulation builds up a galactic disk self-consistently bygas inflow from filaments and mergers and naturally takes intoaccount radial migration processes due to early merger activityand internal disk evolution at low redshift. The last massivemerger takes place at ∼ 9 Gyr look-back-time having a diskmass ratio of 1:5. A relatively quiescent phase marks the last 8-9 Gyr of evolution. A number of less violent events (1:70-1:100mass ratio) are present during this period, with their frequencydecreasing with time. The accreted disk component at the finaltime, estimated at 4 < r < 16 kpc, is ∼ 3% of the total diskmass. In paper I and this work we chemically tag only starsborn in situ and do not consider the accreted stellar component,which would introduce an additional complexity in the chemo-kinematic relations. The exploration of the range of parametersarising from considering the accreted component is deferred toa future work.

A central bar develops early on, doubles in size in the last∼ 6 Gyr, and has a similar length at the final simulation timeto that of the MW (see paper I, Fig. 1 rightmost top panel).Snapshots of the disk face-on and edge-on stellar surface den-sity can be seen in Fig. 1 of paper I. An important ingredient,which ensures we capture disk dynamics similar to the MW, isthat prior to inserting the chemical evolution model, we rescalethe simulation to place the “solar radius” (8 kpc) just outsidethe 2:1 outer Lindblad resonance (OLR) of the bar, as is be-lieved to be the case for the MW (e.g., Dehnen 2000; Minchevet al. 2007, 2010). Consideration of the bar when studying theMW disk is important, since the bar is expected to dominate thedisk dynamics within 2-3 scale-lengths through its corotationresonance (CR) and OLR, may drive spiral structure of differ-ent multiplicity (e.g., Masset and Tagger 1997; Quillen et al.2011; Minchev et al. 2012b), and be responsible for couplingbetween the vertical and radial motions at preferred locationsboth in the inner (Combes et al., 1990; Quillen et al., 2014) andthe outer disk (Minchev et al., 2012a).

1.2. Need for chemo-kinematics information of theentire disk

While a range of models may be able to match the chemo-kinematics of stars in the solar neighborhood, discriminationbetween different evolution scenarios can be made by requiringthat models are compliant with data covering extended portionsof the disk. By integrating the orbits of RAVE giants, Boeche

et al. (2013b) were able to cover extended disk radii by consid-ering the guiding radii, instead of the current stellar positions.SEGUE G-dwarf data has also been used to cover disk regionsbetween 6-12 kpc (Cheng et al., 2012b; Bovy et al., 2012b).Large portions of the Galactic disk close to the plane are nowobserved with APOGEE (Anders et al., 2014; Hayden et al.,2014).

Variations of chemical gradients are expected for differentage populations, as well as for different vertical slices of thedisk. A realistic MW chemo-dynamical model must be ableto explain not only the local properties of stars but also thesevariations with Galactic radius and distance from the disk mid-plane. The goal of this work is to extend the results of paper I toregions beyond the solar vicinity, by using the same model, andprovide understanding for the causes of the expected variations.We note, however, that a direct comparison between the resultspresented here and observational data must be done with care,as observational biases can affect strongly chemo-kinematic re-lations, especially at large distances. A future work will be ded-icated to the proper comparison to observations with the helpof mock catalogues constructed from our models (Piffl et al., inpreparation).

2. Effects of radial migration in our simulationIn paper I (Fig. 1, bottom panel) we showed the changes in an-gular momentum at different stages of the disk evolution. Thisrevealed that the strength and radial dependence of migrationis governed by merger activity at high redshift and internal per-turbations from the bar and spirals at later times.

Another way of looking at the mixing induced throughoutthe galaxy lifetime is presented in Fig. 1, where the top rowshows density contours of stellar final radii, r f inal, versus birthradii, r0, at the end of the simulation. The contour level separa-tion is given on top of the left row. The inner 1-kpc disk is notshown, in order to display properly the contours. The disk isdivided into six age groups, as specified on top of each panel.The dotted-red and solid-blue vertical lines indicate the posi-tions of the bar’s CR and OLR at the end of the simulation.The dashed-black line shows the locus of non-migrating circu-lar orbits. Deviations from this line are caused not only fromstars migrating from their birth places, but also from stars oneccentric orbits away from their guiding radii. The latter ef-fect becomes more important with increasing age, especiallyfor stars with age > 8 Gyr, e.g., those formed before the lastmassive merger event in our simulation.

To exclude the effect of high-eccentricity stars, in the bot-tom row of Fig. 1 we show the density of final versus birthguiding radii, rg, f inal and rg,0, respectively. We estimate thesefor each stellar particle as

rg,0 =L0vc,0

(1)

and

rg =Lvc, (2)

where L0 ≡ r0vφ,0 and L ≡ rvφ are the initial and final angularmomenta, respectively, while vc,0 and vc are the initial and final

I. Minchev et al.: Chemodynamical evolution of the Milky Way disk II 3

0<age<2 Gyr 2<age<4 Gyr 4<age<6 Gyr 6<age<8 Gyr 8<age<10 Gyr age>10 Gyr

Fig. 1. Top: Actual birth radii versus final radii for stars in different age bins as indicated in each panel. The dotted-red and solid-blue verticallines indicate the positions of the bar’s CR and OLR. The dashed black line shows the locus of non-migrating circular orbits. Bottom: Guidingbirth radii versus guiding final radii. Using the guiding radii excludes the effect of high-eccentricity stars, thus exhibiting better the resonantlocations as clumps along the dashed black line. The effect of the bar is seen in the overdensity inside the CR, indicating stars shifted preferen-tially from their radius outward in the disk. This becomes more evident for younger stars due to their colder orbits, allowing them to respondmore strongly to the perturbations.

values of the circular velocity at the corresponding radii, whichchanges roughly between 190 and 220 km/s, while remainingsignificantly flat except for the decline at r < 1.5 kpc (see toprow of Fig. 1 in paper I).

Several interesting differences are seen between the stellardistributions in the r0− r f inal and rg,0− rg, f inal planes. Firstly wefind that all guiding radius distributions are much more sym-metric around the dashed-black line, indicating more balancedexchange of particles across a given disk radius. This is be-cause the asymmetric drift effect, where outer radii are popu-lated by high-eccentricity stars close to their apocenters, hasbeen removed by using the guiding radii. Another difference isthe better identification of efficient migration radii in the guid-ing radii plots (such as the bar’s CR and OLR radii indicated bythe dotted-red and solid-blue verticals). Note that these becomemore clear for younger (and thus colder) populations, becausecolder orbits respond more strongly to the non-axisymmetricperturbations (e.g., spirals and bar). Interestingly, a well de-fined peak is found inside the bar’s CR for the oldest stellarcomponent when we use the guiding radii. While some of thesestars have gained angular momentum already during the strongmerger phase ending in the first 2-3 Gyr of evolution, the peakbecomes well defined only after the bar is formed, as seen inmiddle row, left panel of Fig. 15 in paper I. This indicates thatthe bar affects not only the stars born after its formation, butalso the oldest stars, as should be expected.

In both rows of Fig. 1 we find that the largest width aroundthe black-dashed line occurs for stars in the age groups 4 <age < 6 and 6 < age < 8 Gyr. This is indicative of largechanges in angular momentum related to significantly long ex-posure to migration mechanisms. The two oldest populations

do not migrate as much because of their high velocity disper-sions resulting from the high-redshift merger phase.

A decrease in disk scale-length is apparent with increasingage, ending up with a very concentrated disk for ages >10 Gyr.This is in agreement with observations in theMW (e.g., Bensbyet al. 2011; Bovy et al. 2012b) and will be discussed more inSec. 4.3. The effect of the bar is seen in the overdensity insidethe CR (dotted-red vertical), indicating stars shifted preferen-tially from their birth radii outward in the disk.

2.1. Migration cools the disk during mergers

We showed in paper I that stars born in the inner disk can ar-rive at the simulated solar vicinity with lower velocity disper-sion than the in-situ born population. This is in drastic con-trast to the expected effect of outward migrators in a quiescentdisk evolution, where stars arriving from the inner disk areslightly warmer than the non-migrating population (Minchevet al., 2012a). Below we investigate this in grater detail study-ing the entire disk.

First we consider all stars born right before the last mas-sive merger encounters the disk, at t = 1.4 Gyr. To see howmuch angular momentum redistribution takes place during thismerger event, in the top panel of Fig. 2 we plot number den-sity contours of the changes in guiding radius, ∆rg, versusthe initial guiding radius, rg,0, estimated in the time period1.4 < t < 3.4 Gyr. The percentage of stars in each contourlevel is given by the color bar on the right.

The strong redistribution of angular momentum seen in therg,0−∆rg plane is caused both by the tidal effect of the satellite,which plunges through the galactic center, and the strong spiral


Fig. 2. The effect of migration during (left) and after (right) a massivemerger. Left column: The top panel shows the changes in angularmomentum in a time period of 2 Gyr encompassing the merger event.The vertical velocity dispersion profiles of inward migrators, outwardmigrators and the non-migrating population, as indicated, are shownin the second panel. The net effect of migrators can be seen in thethird panel. The bottom panel shows the fractional change in velocitydispersion resulting from migration ∆σz = (σz,all − σz,non mig)/σz,all.Migrators cool the outer disk, thus working against disk flaring.Rightcolumn: Same as on the left, but for stars born after the last massivemerger event. Minimal effect from migration is seen on the disk verti-cal velocity dispersion.

structure induced in the gaseous component. We note that thedisk dynamics is dominated by the very massive gas disk at thisearly stage of disk evolution.

Next we separate migrating from non-migrating stars (inthe considered time period) by applying the technique de-scribed by Minchev et al. (2012a). This consists of separatingstars in a given radial bin into ”migrators” and ”non-migrators”as follows. Non-migrators are those particles found in the se-lected radial bin at both the initial and final times, while mi-grators are those that were not present in the bin initially butare there at the final time. We distinguish between ”outward”and ”inward” migrators – those initially found at radii smalleror larger than the annulus considered, respectively. This is donefor radial bins over sampling the entire radial extent of the disk.See Minchev et al. (2012a) for more details.

In the second top-to-bottom left panel of Fig. 2 we plotthe vertical velocity dispersion profiles of inward migrators,outward migrators and the non-migrating population, as indi-

cated. It is interesting to see that inward and outward migratorsduring the merger have reversed roles, where stars migratinginwards have positive contribution to σz and those migratingoutward cool the disk. This is the opposite of what is expectedfor migration in the absence of external perturbations (as de-scribed in the Introduction and shown in paper I). The recentwork by Minchev et al. (2014) showed that the fact that cool,old, [α/Fe]-enhanced, metal-poor stars can arrive from the in-ner disk can provide a way to quantify the MWmerger history,where the idea was applied to a high-quality selection of RAVEgiants (Boeche et al., 2013a) and the SEGUE G-dwarf sample(Lee et al., 2011). Indeed, the effect of satellites perturbing theMW disk has been linked to a number of observations of struc-ture in the phase-space of local stars (e.g., Minchev et al. 2009;Gomez et al. 2012b,a, 2013; Widrow et al. 2012; Ramya et al.2012).

The net effect of migrators duringmerger can be seen in thethird top-to-bottom left panel of Fig. 2. The overall contributionto the vertical velocity dispersion from the migrating stars dur-ing the merger is negative, in the sense that it is lower than thatof the stars which did not migrate. We emphasize that we onlyconsidered stars born before the merger took pace, therefore,the effect seen is not related to the accreted population.

Finally, to quantify the changes to the disk vertical velocitydispersion resulting frommigration in the given period of time,we plot the fractional changes in the bottom left panel of Fig. 2.We estimate these as

∆σz = (σz,all − σz,non mig)/σz,all, (3)

where σz,all and σz,non mig are the vertical velocity dispersionsfor the total population and the non-migrators, respectively.Decrease in σz of up to 30% can be seen.

We have found here that during a massive merger sinkingdeep into the disk center, migrators cool the outer disk, thusworking against disk flaring. This is related to the stronger ef-fect of mergers on the outer disk, owing to the exponential de-crease in the disk surface density. Stars arriving from the innerparts during a merger, would therefore be cooler than the restof the population.

We now contrast the above results with a sample born af-ter the last massive merger even. The right column of Fig. 2 isthe same as the left one, but for stars born after t = 2.5 Gyr (or8.7 Gyr ago). Minimal effect frommigration is seen on the diskvertical velocity dispersion during the last 2 Gyr of (mostly qui-escent) evolution, despite the strong migration efficiency seenin the top right panel.

In accordance with the above results, small (and mostlynegative) contribution of radial migration on the age-velocityrelation was found also by Martig et al. (2014b), where a suiteof seven simulation similar to the one considered in this workwas studied. Additionally, studying the high-resolution isolateddisk simulation of D’Onghia et al. (2013), the recent work byVera-Ciro et al. (2014) also found minimal effect of migrationon the disk thickening.


3<r<5 kpc 5<r<7 kpc 7<r<9 kpc 9<r<11 kpc 11<r<13 kpc5 k< ppck

Fig. 3. Comparison among the distributions of final guiding radii (rg, f inal, top row), birth guiding radii (rg,0, middle row), and actual birth radii(r0, bottom row) for stars of different age groups ending up in a given radial bin, as indicated. Five final radial bins are considered. Solidblack curves plot the total distribution, while the color-coded curves show the distributions of stars in five different age groups. The dotted-redand solid-blue vertical lines indicate the positions of the bar’s CR and OLR estimated at the final time. The width and peak shift of the totaldistributions are shown in Fig. 4. The significantly narrower distributions of final guiding radii (compared to rg,0) in all age-groups indicate thatmigration is important for stars of all ages.

2.2. Contamination from migration at differentdistances from the Galactic center

We would now like to quantify the radial migration as a func-tion of galactic radius in our simulation. For this purpose, inFig. 3 we study the origin of stars ending up in five radial binsof width 2 kpc, centered on r = 3, 5, 7, 9, and 11 kpc. Foreach annulus (green vertical strip), six different age-groups areshown, color-coded in the bottom-leftmost panel. The solid-black line shows the total distribution in each panel. The bar’sCR and OLR are shown by the dotted-red and solid-blue ver-ticals. The middle row corresponds to the solar vicinity (thebottom-middle panel is the same as the left panel of Fig. 3 inpaper I) with the bar’s OLR at 7.2 kpc. Guiding radii for thisfigure are estimated from equations 1 and 2 as in Fig. 1.

In the top row of Fig. 3 we show the final guiding radii,rg, f inal, of stellar particles ending up in the five annuli consid-ered at the final simulation time. This shows that there is a sub-stantial fraction of stars with angular momentum lower (to theleft of the bin) or higher (to the right of the bin) than appropri-ate for the given annulus, but populating that bin close to their

apocenters or pericenters, respectively. The predominancy ofstars with lower angular momenta is related to the well-knownasymmetric drift effect seen in solar neighborhood stars (meanrotational velocity distribution offset to negative values), whichis found here to increase strongly with increasing galactic ra-dius.

In the second row of Fig. 3 we show the birth guiding radii,rg,0, of stars currently in the five bins considered. The distribu-tions widen strongly compared to those shown in the first row,indicating significant changes in angular momentum since theirbirth. The drastic differences found between the distributionsin the first and second rows speak of the importance of angularmomentum redistribution within the disk, i.e., radial migration.We emphasize the strong changes in angular momentum seeneven for the oldest ages (red histograms), although the migra-tion efficiency for these stars is expected to be reduced due totheir larger velocity dispersions (see Fig. 1).

Finally, in the bottom row of Fig. 3 we show the actual birthradii, r0, (not guiding radii) of stars ending up in the final fivebins considered, where we see the effect of both the changes


age >

9 Gyr

age < 9 Gyr

age < 5 Gyr

Fig. 4. Left column: Variation with Galactic radius of the fraction ofstars arriving from the inner disk, from the outer disk, and those nativeto a given radius. Right column: Peak shift and width of the total dis-tributions (black curves). The peak shift of stars born before (red) andafter (blue) the last massive mergers are also shown. From top to bot-tom, different rows show the above quantities estimated for the finalguiding radius (rg, f inal), the guiding birth radius (rg,0), and the actualbirth radius (r0), as in Fig. 3. The peak shift is defined as the differencebetween the median final radius and the peak of the total distributionsshown in Fig. 3. The width is estimated as the standard deviation ofthe total distribution in each bin. For this figure we consider 30 over-lapping radial bins instead of the five used in Fig. 3, in order to betterexhibit the radial variations.

in angular momentum and heating. Distributions are similar tothose of the initial guiding radii, rg,0, shown in the second row.

While Fig. 3 can be interpreted as giving an account for(1) stars appearing in a given radial bin close to their apo- andpericenters (first row) and for (2) stars which have migratedthere (middle row), it must be realized that the situation is morecomplicated than that. Even stars with guiding radii outside thegiven radial bin have experienced radial migration. Therefore,those cannot be treated simply as non-migrators contaminatinga given radius because of large eccentricities as it is frequentlydone in the current literature. An evidence that even the oldestand, thus, the hottest stars have migrated substantially is givenby the differences seen in the red histogram in the top and mid-

dle rows of Fig. 3, where the initial guiding radii cover a muchlarger radial extent than the final guiding radii.

To quantify better the amount of migration and heating seenin Fig. 3, in Fig. 4 we plot the radial variation of the fraction ofstars arriving from the inner disk, from the outer disk, and thosenative to a given radius (left column), as well as the peak shiftand width of the distributions (right column). The peak shift isdefined as the difference between the median final radius andthe peak of the total distribution shown in Fig. 3. The width isestimated as the standard deviation of the total distribution ateach annulus.

As in Fig. 3, the three rows of Fig. 4, from top to bottom,correspond to rg, f inal, rg,0, and r0. To see better the radial varia-tion of the above quantities, we have considered 30 overlappingradial bins in the radial range 4 < r < 12 kpc, instead of thefive bins shown in Fig. 3.

Focussing on the top-left panel of Fig. 4, we find an in-crease with increasing distance from the Galactic center, in thefraction of stars with final guiding radii (rg, f inal) inside a givenannulus (red-dashed curve), from ∼35% to ∼60%. Only about10% of stars have guiding radii higher than those appropriatefor a given annulus (blue-solid curve). The fraction of stars withangular momenta just right for a given annulus decreases withGalactic radius from∼55% to∼35% (black-dotted curve). Notethat at the solar radius (8 kpc) the fraction of stars belonging tothe inner disk is similar to that of stars with angular momentatypical for that annulus. It should be kept in mind that the abovenumbers will change if we were to use an annulus width differ-ent than the 2-kpc utilized for Figures 3 and 4.

While we find that a lot of contribution can come from starswith angular momenta lower than that appropriate for a givenradial bin (e.g., ∼ 50% at the solar radius), it is also importantto know how far these stars come from. Therefore, in the top-right panel of Fig. 4 we show the radial variation of the dis-tributions’ peak shift (solid curve) and width (dashed curve).An increase in both of these is found with radius, indicatingstronger contamination in the outer disk.

In the second row of Fig. 4 we show that the fractions ofstars with birth guiding radii (rg,0) coming from the inner orouter disk are appreciably larger than the fraction of stars ar-riving at a given radial bin simply due to their eccentric or-bits (as in the top row). For example, at the solar radius about60% of stars were born in the inner disk, only about 30% wereborn in situ (7 < r < 9 kpc), and about 15% migrated fromthe outer disk. However, in the second-row, right panel, we seethat the peak shift at the solar radius more than doubles andthe width of the distribution is also quite larger than that seenin the final guiding radii. The nonlinear increase with radius ofthe peak shift is related to the variation in migration efficiencywith Galactic radius, as seen in the bottom row of Fig. 1 ofpaper I (see discussion in paper I). The rate of increase in con-tamination with radius is higher for the birth guiding radii thanfor the final guiding radii by about a factor of two (compareslopes in black-solid curves in the top and middle panels in theright column of Fig. 4).

Finally, the bottom row of Fig. 4 shows the fraction of stel-lar actual birth radii (r0) contributing to different radial bins.This can be seen as the effect of both migration and heating,


Fig. 5. Top row: Color contours show the age-[Fe/H] relation for the same disk annuli as in Fig. 3. The middle row (7 < r < 9 kpc) correspondsto the solar neighborhood. The input chemistry, native to each bin, is shown by the solid-green curve. The dashed-pink curve indicates the mean[Fe/H] binned by age. The gradient is only weakly affected at and inward of the solar circle. Second row: [Fe/H]-[Mg/Fe] stellar distributions.As in the top row, the input chemistry is shown by the solid-green curve. Third row: Metallicity distributions. In addition to the total sampleat each radial bin, the color-coded curves indicate groups born at different galactic radii. In each panel, the thick curve shows the stars born inthat given radial bin.

but note that it is not simply the addition of the top two rowssince, for example, some stars with guiding radii appropriatefor a given radial bin can be found outside that annulus at agiven time. The bottom row of Fig. 4 is similar to the middlerow, with somewhat higher fraction of stars arriving from theinner disk (red-dashed curve in left panel) and yet steeper in-crease in the peak shift (black-solid curve in right panel).

As mentioned earlier and seen in Fig. 3, the oldest starsare the ones most affected by radial migration processes. Toillustrate this and contrast the effect of migration and heatingon young and old stars, in the right column of Fig. 4 we over-plotted the peak shift variation with radius of stars born beforethe last massive merger (ages> 9 Gyr, solid-red curve), starsborn after the last massive merger (ages< 9 Gyr, solid-greencurve), and stars with age< 5 Gyr (solid-blue curve). It is no-table that (i) the increase of the peak shift with radius for theyounger stellar populations is also quite strong and (ii) the ef-fect is significantly stronger when migration and heating acttogether – a maximum of ∼ 1.6 kpc shift is found for r 0 (bot-tom panel), while the effect of heating only, indicated by r g, f inal,reaches ∼0.85.

The predicted increase in contamination from migrationand heating with radius is due to the exponential drop in disksurface density, where more stars are available to migrate out-wards than inwards. Note that inward migration is still veryimportant both for the kinematics and chemistry, in that starsarriving from the outer disk balance the effect of stars com-ing from the inner disk at intermediate radii (as discussed inSections 3.1 and 4.4).

As may be expected at this point, this difference in contam-ination from radial migration and heating at different galacticradii should have strong effect on the disk final chemistry. Weanticipate these effects to be now testable with the large body ofdata coming from current Galactic spectroscopic surveys. Weshow the implication of this in the following sections.

3. Radial variations of chemodynamical relations

3.1. Age-Metallicity Relation at different radiiThe first row of Fig. 5 plots age-[Fe/H] stellar density contoursfor the same disk annuli as in Fig. 3. Contour levels are in-dicated in the color-bar attached to the rightmost panel. The


3 < r < 5 kpc 5 < r < 7 7 < r < 9 9 < r < 1111 < r < 13

|z|<3 kpc

Fig. 6. Left: The mean [Fe/H] variation with age at different Galacticradii as color-coded. Identical to the pink-dashed curves in the top rowof Fig. 5.Right: The mean [Fe/H]-[Mg/Fe] relation for different radii.Same as pink-dashed curves in the secind row of Fig. 5.

middle panel (7 < r < 9 kpc) corresponds to the solar neigh-borhood and is the same as the plot shown in Fig. 4 of paper I.The input chemistry, native to each bin, is shown by the green-solid curve. The pink dashed curves indicate the mean [Fe/H]in each panel. Measurement uncertainties of ±0.1 dex drawnfrom a uniform distribution are convolved with our simulated[Fe/H].

While a scatter in the age-metallicity relation (AMR) isseen at all radii, the mean (pink-dashed curves) is very closeto the local evolution curve in the inner three bins. Only out-side the solar radius do we find significant deviation, with thestrongest flattening in the AMR at the outermost bin (11 < r <13 kpc). This results from the accumulation of outward migra-tors in the outer disk, as seen in Figures 3 and 4. Conversely, atradii close to and smaller than the solar radius the contributionfrommetal-rich stars arriving from the inner disk is mostly bal-anced by metal-poor stars arriving from the outer disk. This isanalogous to the contribution to the velocity dispersion frominward and outward migrators discussed by Minchev et al.(2012a), where the overall effect on the disk heating (and thusthickening) was found to be minimal at radii less than aboutfour disk scale-lengths. Similar effect results for the gas (asdiscussed in Sec. 4.4, see Fig. 12), rendering recycled gas flowsunimportant in the range 4 < r < 12 kpc.

The left panel of Fig. 6 shows the mean [Fe/H] variationwith age at different Galactic radii as color-coded. These curvesare identical to the pink-dashed curves in the top row of Fig. 5.

Another important property of the AMR predicted by ourmodel is that the maximum metallicity achieved in each bindecreases from [Fe/H]∼0.5-0.6 to about ∼0.2, as one movesfrom the innermost towards the outermost radial bins. The ex-act amount of metal rich stars predicted by our model is sen-sitive to the initial chemical model assigned to the inner re-gions of the disk. As discussed in paper I, we extrapolated ourthin-disk chemical evolution model to the Galactic center inthe innermost 2 kpc, not assigning a specific bulge chemistryto particles born in that region. This is here justified by the factthat we first want to study the effect of migration in a pure disk.The impact of considering bulge chemistry will be studied ina forthcoming paper. We anticipate that this would mostly af-fect the predicted fraction of super-metal-rich stars in the radialbins internal to the solar vicinity.

Fig. 7. Left: Overlaid normalized metallicity distributions at differentdistances from the Galactic center (all solid-black histograms in bot-tom row of Fig. 5). The peak of the total distribution for each radial binis always centered on [Fe/H]≈ −0.15 ± 0.06 dex and the metal-poorwings are nearly identical, extending to [Fe/H]≈ −1.3 dex. In con-trast, the metal-rich tail of the distribution decreases with increasingradius, giving rise to the expected decrease in mean metallicity withradius. Right: As on the left but for [Mg/Fe]. Similarly to [Fe/H], thepeak does not vary significantly as a function of Galactic radius, beingsituated at [Mg/Fe]≈ 0.15 ± 0.08 dex. Unlike the metallicity distribu-tion, the α-poor tail is lost as radius increases, while the α-rich tailalways ends at [Mg/Fe]≈ 0.45 dex. However, the correspondence be-tween [Fe/H] and [Mg/Fe] is not symmetric: for [Mg/Fe] both wingsof the distribution are affected and the width decreases with increasingradius. See Fig. 9 for variation with distance from the disk plane.

The fraction of stars with metallicities above ∼0.2-0.3 dex can be used as a powerful constraint of our mod-els. Observationally, it is still difficult to quantify this fractionnot only due to observational biases induced by color-selectedspectroscopic samples, but also because of difficulties of cur-rent abundance pipelines to account for metallicities above so-lar. This situation will certainly improve in the future as spec-tral libraries and stellar isochrones get extended beyond solar.

3.2. [Fe/H]-[Mg/Fe] relation at different radii

The second row of Fig. 5 shows [Fe/H]-[Mg/Fe] density con-tours. Uncertainties of ±0.1 and ±0.05 dex (typical of high-resolution observations in the literature) drawn from a uni-form distribution are convolved with our simulated [Fe/H] and[Mg/H] abundances, respectively1.

An overall contraction in [Mg/Fe] is found with increasinggalactocentric distance, due to the decrease of high-metallicitystars in the outer bins as well as the decrease of high-[Mg/Fe]stars.

In the model, most of the super-metal-rich stars originatingin the innermost disk regions (see gold contours) are predictedto have sub-solar [Mg/Fe] ratios. The exact amount of this ef-fect (i.e., the absolute values of [Mg/Fe] at a different [Fe/H])is strongly dependent on the adopted stellar yields of Mg, Feand the SNIa rates (here we adopt the same stellar yields as inFrancois et al. 2004). How stellar yields behave at above so-

1 These uncertainties are the same as those used for [Fe/H] and[O/H] in paper I, although there it was erroneously stated that±0.05 dex was the uncertainty in [O/Fe]


Fig. 8. Top: Metallicity distributions at different distances from the Galactic center. In each panel the solid black histogram shows the totalsample (same as colored lines in Fig. 7, left), while various colors correspond to different age groups as indicated in the bottom left panel. It isremarkable that despite the strong decrease in the fraction of old stars (red and orange lines), the metal-poor tail remains practically identicalfor samples at different radii (as seen in Fig. 7, left). While in the central regions it is dominated by the oldest stars, in the outer disk it is amixture of all ages. Bottom: Same as above but for [Mg/Fe]. Here the decrease in the fraction of old stars gives a significant effect in the α-richwing of the distribution (see Fig. 7, right).

lar metallicity regimes is still very uncertain. Improvements onstellar evolution models at very high-metallicities are on theway by several groups, and will be soon implemented in ourmodels as well.

As a summary of the second row of Fig. 5, the left panelof Fig. 6 shows the variation of the mean [Fe/H]-[Mg/Fe] re-lation with Galactic radius as color-coded. These curves areidentical to the pink-dashed curves in the second row of Fig. 5.Only small variations are found, mostly at super-solar values of[Mg/Fe].

We do not find a bimodality in the [Fe/H]-[Mg/Fe] at anydistance from the Galactic center. We showed in paper I that thedistribution at the solar radius can become bimodal when selec-tion criteria used in high-resolution surveys (e.g., Bensby et al.2003) were applied (see paper I, Fig. 12). It should be notedthat the gap in [α/Fe] (usually ∼ 0.2 dex) has now been seenin a number of different observational samples (e.g., SEGUE- Lee et al. 2011, APOGEE - Anders et al. 2014, HARPS -Adibekyan et al. 2013, GES - Recio-Blanco et al. 2014) indi-cating that it may be a real feature and not just a selection bias.

Several studies of the [Fe/H]-[α/Fe] plane (e.g., Bensbyet al. 2011; Cheng et al. 2012a; Anders et al. 2014) haveshown that the number of high-[α/Fe] metal-poor stars de-creases strongly in the outer disk. A work in preparation isdedicated to the proper comparison with observations, wheresurvey biases will be considered when comparing to our model.However, a decline in themaximumvalue of [Mg/Fe] is alreadyclearly seen in the second row of Fig. 5 - a shift downward in[Mg/Fe] of ∼ 0.2 dex is found in the three densest contours,when comparing the innermost to the outermost radial bins.

Introducing a gap at ∼ 0.2 dex (as discussed above), whichwould result naturally from a gap in the star formation at highredshift (as in the two-infall model of Chiappini et al. 1997),may naturally improve the comparison between our model andthe observations.

3.3. [Fe/H] and [Mg/Fe] distributions at different radii

The third row of Fig. 5 shows the metallicity distributions atdifferent distances from the Galactic center. In each panel thesolid-black histogram shows the total sample, while variouscolors correspond to groups of common birth radii, as indi-cated on the left. The thick histogram in each panel shows starsborn in that given radial bin, e.g, green corresponds to the solarvicinity.

In all final radial bins the metal-rich tail of the distributionresults from stars originating in the inner disk (compare thelocal metal-rich tail to that of the total distribution). Note thatthe largest contribution in the range 7 < r < 11 kpc (the solarbin and the neighboring two bins) to the metal-rich tail comesfrom the bar CR region (blue curve). Therefore, the existenceof a metal-rich tail throughout most of the disk can be linked tothe effect of the MW bar. This was already noted in paper I forthe solar vicinity (see bottom row of Fig. 1 of that work).

For better comparison of the [Fe/H] distributions at differ-ent distances from the Galactic center (solid black histogramsin the bottom row of Fig. 5), in the left panel of Fig. 7 we showthese overlaid and color-coded, as indicated in the right panel.We find that the peak of the total distribution for each radial binis always centered on [Fe/H]≈ −0.15± 0.06 dex and the metal-


poorwings are nearly identical, extending to [Fe/H]≈ −1.3 dex.In contrast, the metal-rich tail of the distribution decreases withincreasing radius, giving rise to the expected decrease in meanmetallicity with radius. This is a property of the chemical evo-lution model used, as evident from examining the locally bornstars in each annulus in the bottom panel of Fig. 5. However,we can also see clearly that for each annulus the metal-rich tailis extended (in each case by about 0.2-0.3 dex) because of starsmigrating from the inner disk. As shown later in Fig. 9, thisresults from stars close to the disk midplane - another evidencethat outward migrators do not populate a thick disk.

The right panel of Fig. 7 is like the left one but for [Mg/Fe].Similarly to [Fe/H], the peak does not vary significantly as afunction of Galactic radius, being situated at [Mg/Fe]≈ 0.15 ±0.08 dex. In this case the α-poor tail is lost as radius in-creases, while the α-rich tail always ends at [Mg/Fe]≈ 0.45 dex.However, the correspondence between [Fe/H] and [Mg/Fe] isnot symmetric: for [Mg/Fe] both wings of the distribution areaffected. In both cases the distributions get broader with in-creasing radius, which is a testable prediction with currentGalactic spectroscopic surveys.

To see what ages comprise different regions of the [Fe/H]and [Mg/Fe] distributions, in Fig. 8 we decompose them intosix different age groups, as indicated in the bottom left panel.It is remarkable that despite the strong decrease in the fractionof old stars (red and orange lines) with increasing radius, themetal-poor tail remains practically identical for samples at dif-ferent radii (as seen in Fig. 7, left). While in the central regionsit is dominated by the oldest stars, in the outer disk it is a mix-ture of all ages.

In the bottom row of Fig. 8 we see that the decrease in thefraction of old stars with increasing radius gives a significanteffect in the α-rich wing of the distribution (see Fig. 7, right).On the other hand, the α-poor tail becomes more prominentin the inner radial bins due to the contribution of the youngeststars (with ages below 3-4 Gyr, born inside the solar circle; seealso Fig. 8).

The strong decrease of the fraction of old/[Mg/Fe]-richstars with Galactic radius seen in Fig. 8 indicates that in ourmodel the age/chemically defined thick disk has a shorter scale-length than the thin disk. This is in agreementwith observationsin the Milky Way (e.g., Bensby et al. 2011; Anders et al. 2014;Bovy et al. 2012b) and will be discussed further in Sections 4.3and 5.

4. Variations with distance from the disk midplaneIn the previous sections we showed general chemodynamicalproperties of our Galactic disk model by analyzing all parti-cles confined to 3 kpc vertical distance from the plane (wheremost of the disk particles lie and current surveys cover). In thissection we consider different cuts in the vertical direction.

4.1. [Fe/H] and [Mg/Fe] distributions at differentheights

We showed in Fig. 7 how the [Fe/H] and [Mg/Fe] distributionsvary with distance from the Galactic center. Because the high-

Fig. 9. Left column:Overlaid normalized metallicity distributions fordifferent distances from the Galactic center for stars with |z| < 0.5 kpc(top) and 0.5 < |z| < 3 kpc (bottom). This shows that variations in themetal-rich end seen in Fig. 7 come mostly from stars close to the diskmidplane. Right column: As on the left but for [Mg/Fe]. Similarly to[Fe/H], strong variations with radius are seen mostly for stars close tothe disk midplane. The reason for this is that migrating stars stay withcool kinematics (both in the radial and vertical directions), i.e., do notcontribute to thick disk formation.

[Fe/H] and low-[Mg/Fe] tails come from stars migrating fromthe inner disk, it is interesting to find out how this is reflectedin samples at different distances from the disk plane.

Similarly to the left panel of Fig. 7, in the left column ofFig. 9 we show normalized metallicity distributions for dif-ferent distances from the Galactic center, but for stars with|z| < 0.5 kpc (top) and 0.5 < |z| < 3 kpc (bottom). We find thatvariations in the high-[Fe/H] tail seen in Fig. 7 come mostlyfrom stars close to the disk midplane. The right column ofFig. 9 is the same as the left one, but for [Mg/Fe]. Similarly to[Fe/H], strong variations with radius are seen mostly for starsclose to the disk midplane. The reason for this is the fact thatstars close to the disk are not just vertically cool, but also theireccentricities are low. Stars with low eccentricities are also theyoungest (on the average), and thus the most metal-rich pop-ulation (on the average). In contrast, the older/hotter popula-tion reaching high distances away from the plane is metal-poor.Note that if stars heated the outer disk as they migrate outwards(i.e., if they populated regions high above the disk midplane)there would not be a difference in the samples close and awayfrom the disk plane, and thus no negative vertical metallicitygradient as seen in a number of observations (e.g., Carraro et al.1998; Chen et al. 2011; Kordopatis et al. 2011).

The age-[Fe/H] and [Fe/H]-[Mg/Fe] relations, as well as thecorresponding distributions for stars with |z| < 0.5 and 0.5 <|z| < 3 kpc are shown in Figures B.1 and B.2 in appendix B.


Fig. 10. Variation of azimuthally averaged chemical gradients with distance from the disk midplane. Top row: Thick black curves show themetallicity variation with galactic radius for stellar samples at different distances from the disk midplane, as marked in each panel. Differentcolors correspond to different age groups as indicated in the bottom-left panel. The height of rectangular symbols reflects the density of eachbin. The negative gradient seen in the total population (leftmost panel) is strongly flattened (and even reversed at r < 10 kpc) for the range0.5 < |z| < 1.0 kpc. Bottom row: Same as above but for [Mg/Fe]. Here the weak positive gradient for the total population (leftmost panel)turns negative as distance from the disk plane increases, although the gradient of each individual age-bin is positive. This figure illustrates thatdifferent mixtures of stellar ages (e.g., because of different slices in z) can give rise to a range of different [Fe/H] and [α/Fe] gradients.

4.2. Chemical gradients at different heights above theplane

Various studies have found different metallicity and [α/Fe] gra-dients in the MW, as discussed in the Introduction. Fig. 10 il-lustrates that different mixtures of stellar ages (e.g., because ofdifferent slices in z) can give rise to a range of different [Fe/H]and [α/Fe] gradients.

Thick black curves in the top row show the azimuthally av-eraged metallicity variation with galactic radius for stellar sam-ples at different distances from the disk midplane, as marked ineach panel. Different colors correspond to different age groupsas indicated in the bottom-left panel. The height of rectangu-lar symbols reflects the density of each bin. The bottom row ofFig. 10 shows the same information as above but for [Mg/Fe].

The negative radial metallicity gradient seen in the totalpopulation (leftmost upper panel) is strongly flattened with in-creasing |z|, and even reversed at r < 10 kpc for the range0.5 < |z| < 1.0 kpc. By examining the variation in densityof different age subsamples, we see that the change in slopewith increasing |z| is caused by the strong decrease of stars withages < 6 Gyr at |z| > 0.5 kpc for r ! 12 kpc.

Focusing on [Mg/Fe] we find that the weak positive gradi-ent for the total population (leftmost bottom panel in Fig. 10)turns negative as distance from the disk plane increases, al-though the gradient of each individual age-bin is positive.

In contrast to the strong variation of chemical gradientswith distance from the disk midplane for stars of all ages, thegradients of individual age groups do not vary significantlywith distance from the plane (see Table 1). Gradients in the to-tal population can vary strongly with |z| because of the interplaybetween (i) the predominance of young stars close to the disk

plane and old stars away from it (as illustrated by the rectangu-lar symbols in Fig. 10), (ii) the more concentrated older stellarcomponent (as seen in Fig. 11 below), and (iii) the flaring ofmono-age disk populations (see Martig et al. 2014a, Fig. 5).

The above discussion suggests that the results of differentGalactic surveys should be compared with care, taking into ac-count the spatial andmagnitude coverage of observational sam-ples. Indeed, before large spectroscopic surveys were in place,most of the MW abundance gradients reported in the litera-ture were obtained by using rather young populations, such asCepheids (e.g., Andrievsky et al. 2002; Pedicelli et al. 2009;Luck and Lambert 2011; Lemasle et al. 2013), HII regions(e.g., Daflon and Cunha 2004; Stasinska et al. 2012 and ref-erences therein) and the more numerous young open clusters(e.g., Jacobson et al. 2011; Yong et al. 2012; Frinchaboy et al.2013). The advantage of these young population tracers is thatthey cover a large radial disk extent and are mostly located inthe disk midplane, i.e., lie in a very low z-range. It is clear fromFig. 10 that such young tracers will yield steeper metallicitygradients than a mixed population.

The situation changes when using field stars of mixed ages.In addition the the very local GCS, populations of mixed ageswere covered in larger regions around the solar neighborhoodthanks to RAVE and SEGUE. Using data from the latter twosurveys, it became possible to infer abundance gradients offield stars at high distances from the plane (although most ofthe region near the Galactic plane, i.e., |z| < 0.2-0.4 kpc isnot sampled in this case, see Cheng et al. 2012b; Boeche et al.2013b, 2014). Recently, abundance gradients for field stars (allages covering vertical distances from zero to beyond 3 kpc arebeing estimated thanks to the SDSS-APOGEE survey (Hayden


|z| < 3 kpc |z| < 0.25 kpc 0.25 < |z| < 0.5 kpc 0.5 < |z| < 1.0 kpc 1.0 < |z| < 3.0 kpc[Fe/H], [Mg/Fe] [Fe/H], [Mg/Fe] [Fe/H], [Mg/Fe] [Fe/H], [Mg/Fe] [Fe/H], [Mg/Fe]

age < 2 Gyr −0.058, 0.028 −0.057, 0.027 −0.059, 0.028 −0.064, 0.030 −0.077, 0.0382 < age < 4 −0.048, 0.021 −0.047, 0.021 −0.048, 0.021 −0.049, 0.021 −0.070, 0.0334 < age < 6 −0.040, 0.015 −0.040, 0.015 −0.038, 0.014 −0.041, 0.015 −0.058, 0.0236 < age < 8 −0.039, 0.012 −0.038, 0.012 −0.037, 0.011 −0.038, 0.011 −0.050, 0.0168 < age < 10 −0.031, 0.007 −0.032, 0.008 −0.028, 0.007 −0.030, 0.007 −0.032, 0.007age > 10 −0.022, 0.002 −0.025, 0.004 −0.012, 0.001 −0.020, 0.002 −0.020, 0.001All ages −0.016, 0.003 −0.027, 0.009 −0.012, 0.001 −0.004,−0.004 −0.006,−0.003

Table 1. Gradients in [Fe/H] and [Mg/Fe] (dex kpc−1) for different age populations and distances from the disk midplane, corresponding toFig. 10. Radial range of 5 < r < 13 kpc was used for fitting. For a given age subsample, only minimal variations are seen with distance fromthe disk. However, gradients in the total population can vary strongly due to (i) the predominance of young stars close to the disk plane and oldstars away from it (as illustrated by the rectangular symbols in Fig. 10) and (ii) the more concentrated older stellar component. It should be keptin mind that the variations of [Fe/H] and [Mg/Fe] with radius are rarely well fitted by a single line in both the observations and our model (seeFig. 10). Therefore, non-negligible variations in the estimated gradients should be expected with a change in the radial range used for fitting.

et al., 2014; Anders et al., 2014) – an infrared high-resolutionsurvey that can observe stellar populations very close to thegalactic plane, filling the gap left by SEGUE and RAVE. Notethat in GCS, RAVE, SEGUE and APOGEE, the age mix is notonly a strong function of the distance from the plane and fromthe galactic center, but also dependent on the selection biasesof each sample.

Given the above discussion, we do not show in the presentpaper a direct comparison of the magnitude of our predictedgradients with observations. The main focus here is to under-stand what is driving the general shape of the abundance gra-dients given the different mix of ages of the tracer populationsat different heights from the plane. However, we can say thatthe [Fe/H] gradients predicted for our youngest population bin(< 2 Gyr), in the range 5 < r < 13 kpc (see Table 1) are ingood agreement with the values reported in the literature forCepheids (e.g., Lemasle et al. 2013) and young open clusters(Frinchaboy et al., 2013) of around−0.06 dex/kpc. For [Mg/Fe]we predict a positive gradient of ∼ 0.03 dex/kpc for stars withage < 2 Gyr, which could be in slight tension with the observa-tions of young populations showing almost flat [Mg/Fe] gradi-ents (e.g., Jacobson et al. 2011). Our values for ”all ages” alsocomparewell with the recent values reported in the literature byBoeche et al. (2013b) and Anders et al. (2014), based on RAVEand APOGEE data, respectively, both for iron and [α/Fe] gra-dients. A more detailed comparison with RAVE and APOGEEdata is deferred to a future work, where we will take properlyinto account the spatial and magnitude coverages (along withthe expected sample biases).

It should also be kept in mind that the variations of [Fe/H]and [Mg/Fe] with radius are rarely well fitted by a single linein both observations and our model. Therefore, non-negligiblevariations in the estimated gradients should be expected with achange in the radial range used for fitting.

4.3. Disk scale-lengths at different heights above theplane

We now examine the variation of disk scale-length with dis-tance from the disk plane for populations grouped by commonages or chemistry.

The first row of Fig. 11 shows stellar surface density as afunction of galactic radius for stars with distance from the mid-plane |z| < 3 kpc. In addition to the total mass (pink symbols),stars grouped by six bins of age (left panel), [Mg/Fe] (middlepanel), and [Fe/H] (right panel) are shown by different colors.The corresponding bin values are indicated above each panel.The second and third rows of Fig. 11 are the same as the firstone, but for stars with |z| < 0.5 and 0.5 < |z| < 3 kpc, respec-tively. The color-coded values in the left column, r d, indicatesingle exponential fits in the range 5 < r < 16.5 kpc, shown bythe dotted lines (dashed pink line for the total population).

The total density has rd = 2.43 kpc at |z| < 3 kpc, however,depending on the age, values can range from∼ 1.7 to ∼ 3.1 kpc.This smooth increase in scale-length with decreasing age is amanifestation of the disk inside-out growth and is in agree-ment with the results of Bovy et al. (2012b), if we assume thatmono-age populations correspond to mono-abundance popu-lations. Note that despite the significant migration throughoutthe disk evolution (see Figures 1 - 3), older disks do not in-crease scale-lengths fast enough to compete with the naturallyresulting larger scale-lengths for younger populations, due tothe changes in the SFR as a function of radius. Therefore, whilemigration does flatten surface density profiles (e.g, Foyle et al.2008; Debattista et al. 2006; Minchev et al. 2012b), this cannotovertake the effect of inside-out disk growth. Deviations fromthis rule for some intermediate-age populations was reportedby Martig et al. (2014a), possibly related to satellite-disk inter-actions.

Decrease in scale-length is seen with increasing age for allthree distances from the disk plane (Fig. 11, left column). Theyoungest population shows the largest scale-length at 0.5 <|z| < 3 kpc (rd = 5.5 kpc) and the smallest at |z| < 0.5(rd = 2.9 kpc), which indicates that the fraction of young starsat larger radii increased with distances from the disk plane. This


Fig. 11. First row: Stellar surface density as a function of galactic radius for stars with distance from the midplane |z| < 3 kpc. In additionto the total mass (pink symbols), subsamples grouped by narrow bins of age (left panel), [Mg/Fe] (middle panel), and [Fe/H] (right panel) areshown by different colors, as indicated. The corresponding bin values are shown on top of the figure. The color-coded values in each panelindicate the scale-length, rd , fitted as a single exponential in the range 5 < r < 16.5 kpc, shown by the dotted lines (dashed pink line for thetotal population). Decrease in scale-length is seen with increasing age for all three distances from the disk plane. While single exponential fitsare appropriate for mono-age populations (left column), stars binned by [Mg/Fe] or [Fe/H] show truncation (a change to a steeper exponential)around 5-10 kpc for the younger stars (black and blue curves). Second row: Same as above, but for stars with |z| < 0.5 kpc. Third row: Sameas above, but for stars with 0.5 < |z| < 3 kpc. At this distance from the disk plane (similar to SEGUE G-dwarfs), the breaks in the high-[Fe/H]and low-[Mg/Fe] profiles are mostly gone.

suggests that coeval younger populations should flare, e.g., in-crease their scale-height with radius. Indeed, this was shownby Martig et al. (2014a) for the same simulation we study here.

When stars are binned by [Mg/Fe] (top row, middle panel),we see a break in the trends we have found so far. While fornarrow bins of [Mg/Fe] in the range 0.45-0.05 single exponen-tials can still be fit well at r > 5 kpc, this is no longer truefor lower [Mg/Fe] values. The lowest two bins (blue and blacksquares) deviate from the increasing trend in scale-length for

samples with decreasing [Mg/Fe]. A downtrend at ∼ 10 and∼ 5 kpc is found for the blue and black squares, respectively.For the sake of comparison, for these two bins we still fit singleexponentials in the range 5 < r < 10 kpc.

Similar difficulties with fitting single exponentials to thehighest [Fe/H] bins are also found in the right column ofFig. 11. The situation is very similar for stars with |z| > 0.5 kpc(Fig. 11, bottom middle-row panel).


Fig. 12. The effect of recycled gas flows on the input [Fe/H] used in our model: Top row: Fraction of net gas flow (panel a) into 7 disk annuliof width 2 kpc as a function of time (panel a), where negative values correspond to net inflows. Also shown are the fractions of gas migratinginto each bin from inside (i.e., outward migrators, panel b), from outside (i.e., inward migrators, panel c), and gas which does not leave the bins(panel d). Bottom row:Mean metallicity estimated from the total gas mass (panel e), the gas arriving from inside the given bin (panel f), fromoutside the given bin (panel g), and from the gas which stays in the bin (panel h). The overlaid dashed curves in panels (e), (f), and (g) show thenon-migrating gas (same as panel h). Strong deviations from the input chemistry is found for outward and inward flows (by more than 0.5 dex).However, the net effect is drastically reduced as seen in panel (e), where in the range 4 < r < 12 kpc (purple to orange curves) the deviationsfrom the input curves is less than 0.1 dex during most of the time evolution.

As we move away from the disk plane (as in the SEGUEG-dwarf sample, for example), we find that both [Mg/Fe] and[Fe/H] can all be fit reasonably well by single exponentials.However, the correspondence between age and chemistry is notanymore valid for high [Fe/H], low [Mg/Fe] stars, which do notshow large scale-lengths as the youngest stellar age groups.

4.4. Gas flows

We now investigate how radial gas flows may affect our results.In our simulation stellar mass loss is considered by convertingstellar particles to gas throughout the simulation (see Martiget al. 2012). This can be used to estimate the neglect of gasflows in our chemodynamical model, by studying the effect ofthe radial motion of this ”enriched” gas. We considered the gasconverted from stars at each time step and assigned chemistryto it as a function of time and disk radius, similarly to what wedid for the stars in paper I.

Panel (a) in the top row of Fig. 12 shows the fraction of netgas flow per unit of time, into 7 disk annuli of width 2 kpc asa function of time. We estimate this as the difference betweenthe mass of gas coming from the inner disk and gas comingfrom the outer disk, therefore negative values correspond to netinflows. Also shown in the top row are the fractions of gas mi-grating into each bin from inside (i.e., outwardmigrators, panel

b), from outside (i.e., inward migrators, panel c), and the gaswhich does not leave the bins (panel d).

Typically, about 60-70% of gas in each annulus does notmigrate and contributions from the inner and outer disks areabout 20-30%, with generally slightly larger fraction of gasmigrating outward. Exceptions to this rule are found for theinnermost and outermost annuli. Consequently, the net flowsinto the annuli considered are close to zero (panel a), exceptfor the innermost and outermost disk regions. Larger fractionof outward migrating gas is seen during the first couple of Gyrof disk formation, i.e, during the merger epoch.

In the bottom row of Fig. 12 we now show the mean metal-licity estimated from the total gas mass (panel e), the gas arriv-ing from inside the given bin (panel f), from outside the givenbin (panel g), and from the gas which stays in the bin (panel h).The overlaid dashed curves in panels (e), (f), and (g) show thenon-migrating gas (same as panel h).

As expected, strong deviations from the input metallicityare found for outward only, or inward only flows (by more than0.5 dex). However, the net effect is drastically reduced as seenin panel (e), where in the range 4 < r < 12 kpc (purple toorange curves) the deviations from the input curves is less than0.1 dex duringmost of the time evolution. This is caused by thefact that the effects of inward and outward flows mostly cancelin the radial range 4 < r < 12 kpc.


From the above discussion we conclude that our results forintermediate radial distance from the Galactic center (includingfor the solar neighborhoodpresented in paper I) are not affectedto any significant level by the neglect of gas flows. However,gas flows may be affecting our results for the innermost andoutermost radial bins we study in this paper.

We note that inflows of pristine (metal-poor) gas from cos-mic web filaments may contribute at the disk outskirts by de-creasing the metallicity there, as also reasoned by Kubryk et al.(2013). This can counteract the effect of the radial-migration-induced gas flows to the disk outer boundary seen in Fig. 12.On the other hand, increase in density in the inner 2 kpc dueto inward migration of both gas and stars can be expectedto increase the SFH in that region. This in turn can result inhigher chemical enrichment (higher metallicity) counteractingthe flattening of metallicity gradients induced by migration (seeCavichia et al. 2014). It can be argued, therefore, that the ne-glect of gas flows does not have a strong impact on our results.Further work is needed to investigate the above ideas.

5. Fraction and velocity dispersions ofold/high-[Mg/Fe] stars at different radius anddistance from the disk midplane

We here consider the stars in our model with thick-disk-likechemistry. Similarly to Fuhrmann (2011) (see his Fig. 15), weused a definition for the thick disk [α/Fe]< 0.2 dex (here weuse [Mg/Fe]) and considered the volume defined by 7.9 < r <8.1 kpc, |z| < 0.1 kpc. This resulted in a local fraction of thickto total disk mass of 14%, which is somewhat lower than thevalue of 20% estimated by Fuhrmann (2011) for his volume-complete local sample. As the distance from the solar positionin our model increases from 0.1 kpc to 3 kpc, the thick diskmass fraction increases from 14% to 27%. These numbers areshown in Table 2.

We next divided the disk into inner (4 < r < 8 kpc) andouter parts (8 < r < 15 kpc), and considered four differentmaximum distances from the disk midplane, |z|. The thick to to-tal disk mass fractions for different (r, |z|) ranges are displayedin Table 2, where it can be seen that (1) close to the midplanethere is hardly any variation, (2) as |z| increases the fraction ofhigh-[Mg/Fe] stars always increases, and (3) at |z| > 0.5 kpcthe inner disk contains more stars with thick-disk-like chem-istry compared to the outer disk. The overall decrease of high-[Mg/Fe] stars in the outer disk is consistent with the results ofrecent observational studies (e.g., Bensby et al. 2011; Anderset al. 2014; Bovy et al. 2012b), which have shown that thechemically definedMilkyWay thick disk is more centrally con-centrated than the thin disk. In our model this results naturallydue to the smaller disk scale-lengths of older populations (andgiven the correspondence between age and [Mg/Fe]), which wediscussed in Sec. 4.3.

To see the difference between a chemistry- and an age-defined thick disk, in Table 2 we also list the fraction of starswith age> 9 Gyr with respect to the total disk mass. We pickthis age cut because it marks the last massive merger as dis-cussed in paper I and in Sec. 1.1. While at the solar radius sep-aration by [Mg/Fe] and age gives virtually the same thick to

total disk mass fraction as a function of |z|, in the inner disk theage definition results in ∼ 30% more massive thick disk and inthe outer disk in about 20% less massive. This is to say that inour model the age-defined thick disk is more centrally concen-trated than the chemically defined one. In both cases the thindisk is more extended.

We also estimated the vertical velocity dispersions of thechemistry- and age-defined thin and thick disks in each one ofspatial regions defined above. These numbers are also given inTable 2. Increase in velocity dispersion is seen with decreasingGalactic radius, as expected. However, only small variationsare found with vertical distance from the disk midplane (fora given radius), which is consistent with expectation for theMilky Way (Bovy et al., 2012c).

While here we used a purely chemical or age definition ofthe thick disk, it must be kept in mind that the situation is morecomplicated than that, especially outside the solar neighbor-hood. It is still unclear how the centrally concentrated chemi-cally/age defined thick disk in the Milky Way reconciles withthe extended kinematically defined thick disks in observationsof external galaxies.

6. ConclusionsIn this work we investigated how chemo-kinematic relationschange with position in the Galactic disk, by analyzing thechemo-dynamical model first introduced in Minchev et al.(2013) (paper I). The results of paper I were extended beyondthe solar vicinity, considering both variations with Galactic ra-dius and distance above the disk midplane. Our main resultsare as follows:•We demonstrated that duringmergers stars migrating out-

wards arrive significantly colder than the in-situ population(Fig. 2), as first suggested in paper I. This also has the im-portant effect of working against disk flaring. Our results thatstars migrating outwards in the disk cool the locally born popu-lation is in stark contrast to the suggestion that radial migrationcan form a thick disk. The need for massive mergers at highredshift or stars born hot in a turbulent phase (i.e, during theformation of the thick disk) has been indicated in a number ofrecent observational studies as well (e.g, Liu and van de Ven2012; Kordopatis et al. 2013; Minchev et al. 2014).•We investigated the effect of recycled gas flows and found

that in the region 4 < r < 12 kpc the introduced errors in [Fe/H]are less than 0.05-0.1 dex, related to the fact that inward andoutward flows mostly cancel in that radial range.• We show that radial migration cannot compete with the

inside-out formation of the disk, which can be observed as themore centrally concentrated older disk populations (Fig. 11).This is in agreement with recent results from simulations ofspiral galaxies (e.g., Brook et al. 2012; Stinson et al. 2013; Birdet al. 2013) and observations in the MW (Bensby et al., 2011;Bovy et al., 2012b).• Because contamination by radial migration and heat-

ing becomes more evident with increasing distance from thegalactic center, significant flattening (with respect to the in-situchemical evolution) in the age-metallicity relation is found out-side the solar radius. However, at r < 9 kpc the slope of the


Inner disk Near the solar radius Outer disk4 < r < 8 kpc 7.9 < r < 8.1 kpc 8 < r < 15 kpc

Chemistry-defined thick disk: fr[Mg/Fe]>0.2, σz,thin [km/s], σz,thck [km/s]|z| < 0.1 kpc 0.14, 25, 53 0.14, 20, 36 0.13, 16, 33|z| < 0.5 kpc 0.20, 30, 54 0.16, 22, 43 0.16, 17, 34|z| < 1.0 kpc 0.26, 32, 56 0.22, 23, 42 0.19, 19, 35|z| < 3.0 kpc 0.30, 35, 58 0.27, 25, 48 0.25, 20, 40

Age-defined thick disk: frage>9, σz,thin [km/s], σz,thck [km/s]|z| < 0.1 kpc 0.18, 22, 54 0.14, 19, 38 0.09, 16, 40|z| < 0.5 kpc 0.27, 26, 55 0.16, 20, 46 0.11, 17, 41|z| < 1.0 kpc 0.34, 28, 56 0.22, 21, 45 0.14, 18, 42|z| < 3.0 kpc 0.41, 29, 58 0.28, 22, 50 0.20, 19, 45

Table 2. Fraction of thick to total disk mass at different radii and distances from the disk midplane. Two ways of defining the thick disk areused: by chemistry ([α/Fe]< 0.2 dex) and by age (age> 9 Gyr). For each spatial region and thick disk definition three values are given: theaforementioned fraction (fr[Mg/Fe]>0.2 or frage>9), the vertical velocity dispersion of the thin disk (σz,thin), and the vertical velocity dispersion ofthe thick disk (σz,thick).

locally evolving population is mostly preserved, due to the op-posite contribution of inward and outward migrators.•We predict that the metallicity distributions of (unbiased)

samples at different distances from the Galactic center peakat approximately the same value, [Fe/H] ≈ −0.15 dex, andhave similar metal-poor tails extending to [Fe/H] ≈ −1.3 dex(Fig. 7). In contrast, the metal-rich tail decreases with increas-ing radius, thus giving rise to the expected decline of meanmetallicity with radius. This effect results predominantly fromstars close to the plane (Fig. 9).• Similarly to [Fe/H], the [Mg/Fe] distribution always

peaks at ≈ 0.15 dex, but its low-end tail is lost as radius in-creases, while the high-end tails off at [Mg/Fe] ≈ 0.45 dex.• The radial metallicity and [Mg/Fe] gradients in our model

show significant variations with height above the plane due to adifferent mixture of stellar ages (Fig. 10). We find an inversionin the metallicity gradient from negative to weakly positive (atr < 10 kpc), and from positive to negative for the [Mg/Fe] gra-dient, with increasing distance from the disk plane. We relatethis to the disk inside-out formation, where older stellar popu-lations are more centrally concentrated. This indicates the im-portance of considering the same spatial region for meaningfulcomparison between different studies, as well as observationsand simulations.• In contrast to the strong variation of chemical gradients

with distance from the disk midplane for stars of all ages, thegradients of individual age groups do not vary significantlywith distance from the plane (see Table 1). Gradients in thetotal population can vary strongly with |z|. We relate this to (i)the predominance of young stars close to the disk plane andold stars away from it, (ii) the more concentrated older stellarcomponent, and (iii) the flaring of mono-age disk populations.• The [Fe/H] distributions shift peaks from ≈ −0.15 dex

to ≈ −0.3 dex when samples move from |z| < 0.5 to 0.5 <|z| < 3 kpc (Fig. 9). We showed that the strong effect on thehigh-[Fe/H] tail as a function of Galactic radius comes pre-dominantly from the stars closer to the plane, related to boththe chemical model used and the radial migration efficiency.

• Similarly to [Fe/H], the [Mg/Fe] distributions are also af-fected when varying the sample distance from the disk mid-plane. When changing |z| < 0.5 to 0.5 < |z| < 3 kpc, the[Mg/Fe] peaks shift from ≈ 0.1 dex to ≈ 0.15 − 0.25 dex, de-pending on the sample’s distance from the Galactic center.

Finally, we would like to emphasize an important dynam-ical effect that leads to better understanding of what shapeschemo-kinematic relations. We showed in paper I and thiswork, that migration is significant in our simulation for bothstars and gas, which in principle should prevent us from recov-ering the disk chemical history. However, an interesting effectoccurs away from the disk’s inner and outer boundaries, in theregion 4 < r < 12 kpc (∼1.5-4 scale-lengths). In this radialrange material is exchanged across any given radius in such away as to approximately preserve the kinematical and chemicalproperties of the stars and gas that do not migrate, such as stel-lar velocity dispersions (Minchev et al., 2012a) and mean age-[Fe/H] relations (see Figures 5 and 12). Evidence of migrationcan still be found as scatter in the stellar age-[Fe/H] relation orthe presence of low-velocity dispersion, [α/Fe]-enhanced starsin the solar neighborhood (Minchev et al., 2014).

In contrast, at the disk boundaries, stars migrating inwardsaccumulate in the inner disk (innermost one scale-length) andthose migrating outwards accumulate in the disk outskirts (out-side 3-4 scale-lengths). These effects should be possible toidentify in observations, for example hot populations in diskoutskirts if extended disk profiles are caused by radial migra-tion (Minchev et al., 2012a) or flattening in metallicity gradi-ents in the disk outskirts (Sec. 4.4).

The results presented in this work provide tests for sur-veys, such as RAVE, SEGUE, HERMES, GES, LAMOST,APOGEE, Gaia, WEAVE, and 4MOST. However, once again,we emphasize that direct comparison between the chemo-kinematic relations presented here and observational data mayresult in erroneous conclusions. For a proper comparison it isimperative to correct data for observational biases, as done forthe SEGUE G-dwarf sample (Bovy et al., 2012b). Conversely,using the selection function of a given survey, mock observa-tions can be extracted from our models that can be compared


directly with the data, which is our choice of tackling this prob-lem (Piffl et al., in preparation).

Acknowledgements. We thank the anonymous referee for helpful sug-gestion that have greatly improved the manuscript. We also thank G.Cescutti, B. Gibson, B. Famaey, M. Steinmetz, and R. de Jong forfruitful discussions.

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Appendix A: Comparison between the chemicalmodel and simulation SFHs

In Fig. A.1 we compare the SFH (as a function of cosmic time) of thesimulation with that used for the chemical evolution model. Differentcolors correspond to different disk radii, as indicated. Good overallagreement is found for most radii. Some discrepancy can be seen at 2and 4 kpc approximately at t > 3 and t > 5 Gyr, respectively, wherethe simulation SFH is somewhat stronger. On the other hand, at earlytimes the simulation SFH for r ≥ 4 kpc is lower than the chemicalmodel SFH. This means that the disk inside-out growth in somewhatdelayed in the simulation. As discussed in paper I, we have assumedthat these differences between the simulation and chemical model arenot crucial for the dynamics. However, we weight the stars in the sim-ulation to satisfy the SFH in the chemical model, which is importantfor obtaining the correct mixture of populations corresponding to thechemistry.

Appendix B: Variations in chemo-kinematicproperties with radius and distance from thedisk midplane

Figures B.1 and B.2 present similar information to Figures 5 and 8,but for two different distances from the disk midplane, as indicated.For each 2-kpc annulus a sample close to the plane (|z| < 0.5 kpc) andfarther from the plane (0.5 < |z| < 3 kpc) is plotted. The dashed-pinklines in the first two columns show the mean. The decrease in age withGalactic radius can be seen in the densest contour levels (especially at0.5 < |z| < 3 kpc), which do not extend to young ages for the innerradial bins. For the samples away from the plane shifts in the distri-butions are seen to lower birth-radii, lower metallicities and higher[Mg/Fe], as expected for older populations.

We note that the [Fe/H]-[Mg/Fe] plane does not show a discon-tinuity, as frequently seen in observations. We demonstrated in paperI that a kinematically biased samples can give rise to this divisionbetween the thin and thick disks in the solar vicinity. However, as cur-rently debated in the literature (Fuhrmann, 2011; Anders et al., 2014;Bovy et al., 2012a), this gap may not be an artifact, but a real featurereflecting variations in the SFH of the MW disk. If this is confirmed inobservations, it will serve as an additional constraint for our model, re-quiring the modification of its SFH and early chemistry. Except for thechemical discontinuity, no significant changes to the results presentedin paper I and the current work are expected.


Fig. B.1. Predictions for chemo-kinematic properties at different distances from the Galactic center (see also Fig. B.2). For each 2-kpc annulusa sample close to the plane (|z| < 0.5 kpc) and farther from the plane (0.5 < |z| < 3 kpc) is plotted. The dashed-pink lines in the first twocolumns show the mean.


Fig. B.2. As Fig. B.1 but for samples with 9 < r < 11 and 11 < r < 13 kpc.

Chemodynamical evolution of the Milky Way disk II ...

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